A meshless method with enriched weight functions for fatigue crack growth

Duflot, Marc; Hung, Nguyen Dang

doi:10.1002/nme.948

Cited by 139 publications

(78 citation statements)

References 22 publications

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“…This gives the method the ability to achieve good accuracy with relatively coarse meshes. Note that partition of unity has also been applied in a so-called meshfree context, through extrinsic enrichment [19,46], intrinsic enrichment [43] or weight function enrichment [18]. One of the most recent examples for fracture of quasi-brittle materials using meshfree methods with extrinsic enrichment is shown here: [33].…”

Section: Extended Finite Element Methodsmentioning

confidence: 99%

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Derivative recovery and a posteriori error estimate for extended finite elements

Bordas

Duflot

2007

Computer Methods in Applied Mechanics and Engineering

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The goal of this work is to devise a simple and effective local a posteriori error estimate for partition of unity enriched finite element methods such as the extended finite element method (XFEM). In each element, the local estimator is the L2 norm of the difference between the raw XFEM strain field and an enhanced strain field computed by extended moving least squares (XMLS) derivative recovery obtained from the raw nodal XFEM displacements. The XMLS construction is taylored to the nature of the solution. The technique is applied to linear elastic fracture mechanics, in which near-tip asymptotic functions are added to the MLS basis. The XMLS shape functions are constructed from weight functions following the diffraction criterion to represent the discontinuity. The result is a very smooth enhanced strain solution including the singularity at the crack tip. Results are shown for two and three dimensional linear elastic fracture mechanics problems in mode I and mixed mode. The effectivity index of the estimator is always close to 1. and improves upon mesh refinement. It is also shown that for the linear elastic fracture mechanics problems treated, the proposed estimator outperforms one of the superconvergent patch recovery technique of Zienkiewicz and Zhu, which is only C0. Parametric studies of the general performance of the estimator are also carried out.

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Section: Extended Finite Element Methodsmentioning

confidence: 99%

“…We choose to use additional nodes on each side of the crack [18], as shown in Figure 3. This is by no means mandatory to obtain an accurate representation of the discontinuity, but reduces the support size (smoothing length) required for the calculations, and we make use of this technique in all calculations presented in this paper.…”

mentioning

confidence: 99%

Derivative recovery and a posteriori error estimate for extended finite elements

Bordas

Duflot

2007

Computer Methods in Applied Mechanics and Engineering

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130

102

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“…Currently, there are three main methods for avoiding the drawbacks of FEM remeshing [10]. The boundary element method (BEM) dates back to the 60's and reached its peak of popularity in the 80's.…”

Section: Methods For Modelling Cracksmentioning

confidence: 99%

Modelling Surgical Cuts, Retractions, and Resections via Extended Finite Element Method

Vigneron

Verly

Warfield

2004

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2004

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Abstract. We introduce a new, efficient approach for modelling the deformation of organs following surgical cuts, retractions, and resections. It uses the extended finite element method (XFEM), recently developed in "fracture mechanics" for dealing with cracks in mechanical parts. XFEM eliminates the computationally-expensive remeshing that would be required if the standard finite element method (FEM) was used. We report on the successful application of the method to the simulation of 2D retraction. The method may have significant impact on surgical simulators and navigators.

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“…Recently, much effort has been directed towards the application of meshless methods to crack problems to overcome the difficulties in traditional numerical methods [9][10][11][12][13][14][15][16][17][18][19]. Despite clear general progress with these methods, there are still some technical issues in their application to fracture problems, for instance, it is often awkward and an expensive task to refine the nodal arrangement near the crack tip in order to increase the solution accuracy, since the stress results tend to be oscillatory near the crack tip.…”

Section: Introductionmentioning

confidence: 99%

“…However, introducing such an enriched basis in meshless approximations can lead to ill-conditioning of the global stiffness matrix, and special treatments [12,17] have to be used to alleviate this problem. Thirdly, many meshless methods employ the J-integral or contour integral scheme for the calculation of SIF, which is performed as a post-processing step applied to the stress results, such as in the formulations using the FEM described in [15][16][17][18][19] and partition of unity enriched boundary element method (PU-BEM) [21,22]. This is unlike the case with the isoparametric FEM or sub-region mixed variational principle based FEM where the SIF can be directly obtained as part of the solution [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields

Zhuang

Cai

Augarde

2014

Theoretical and Applied Fracture Mechanics

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(2014) 'A meshless sub-region radial point interpolation method for accurate calculation of crack tip elds.', Theoretical and applied fracture mechanics., 69 . pp. 118-125. Further information on publisher's website:http://dx.doi.org/10.1016/j.tafmec.2013.12.003Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Theoretical and Applied Fracture Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Theoretical and Applied Fracture Mechanics, 69, February 2014, 10.1016/j.tafmec.2013.12.003. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractA new meshless sub-region radial point interpolation method (MS-RPIM) is proposed for linear elastic fracture mechanics. The Williams expansions of stress field for mode I/II crack is used as the trial functions in crack tip region, the meshless radial point interpolation is used for the rest of domain, and a mixed variational principle is used for discretisation. In contrast to existing meshless formulations, the present MS-RPIM requires only very few nodes around the crack tip to obtain smooth stress and accurate results and the SIFs can be directly obtained as part of the solution and no additional effort via post-processing.

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A meshless method with enriched weight functions for fatigue crack growth

Cited by 139 publications

References 22 publications

Derivative recovery and a posteriori error estimate for extended finite elements

Derivative recovery and a posteriori error estimate for extended finite elements

Modelling Surgical Cuts, Retractions, and Resections via Extended Finite Element Method

A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields

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